Flow and heat transfer characteristics of structural viscosity fluids

Laminar friction loss and heat transfer characteristics for a non-Newtonian fluid described by a general viscosity function of the structural type have been computed for tube and slit geometries. The model includes most other models for fluids without a yield stress as special cases. The Graetz problem for constant wall temperature and temperature independent properties has been solved, including viscous dissipation, for the transverse and axial temperature distribution. Both momentum and energy transport characteristics are shown to be strongly dependent upon a dimensionless fluid time constant, which characterizes the transition from Newtonian to non-Newtonian shear thinning behavior. A direct and exact analogy between the momentum and energy transport mechanisms is demonstrated for hydrodynamically and thermally fully developed flow, provided the heat transfer rate is represented by a suitably defined Nusselt number.     

Heat transfer in lid driven channels with power law fluids in a hydrodynamic fully developed flow field

We present a finite element numerical study of heat transfer in lid driven channels with fully developed axial flow for non-Newtonian power law fluids. The effect of channel aspect ratio and material properties on temperature distribution and wall heat transfer are studied. The results show that in comparison with Newtonian fluids the shear thinning property of the fluids acts to reduce the local viscous dissipative heating and as a result the axial local fluid temperature is reduced. Applications of the results to scraped-surface heat exchanger design and operation are recommended.     

Shear rates investigation in a scraped surface heat exchanger

The electrodiffusion technique was performed in order to investigate the shear rate on a scraped surface heat exchanger. Microelectrodes were placed inside: the walls of the outer cylinder; the inlet and outlet bowls; the rotor and the blades. Highly viscous Newtonian fluid (Emkarox HV45 solutions) and non-Newtonian model fluid (aqueous solutions of CMC) were used. The electrodiffusion method allowed us to measure wall shear rates. Maximum shear rate was observed at the scraping surface and caused by blades scraping, high shear rate was also measured on the leading edge of the blades. In the other parts of the exchanger, shear rate remained low but the development of Taylor vortices completely modified the scraped surface heat exchangers behaviour inside the surface of the bowls. A dimensionless representation of the friction factor was established for the inner and outer wall surface of the exchanger.     

剪切稀化流体中微粒子聚集行为研究

在化工过程、生物工程等领域中,实现颗粒分离至关重要。通过整合微流控技术、高速显微图像采集技术和数字图像处理技术,探究微粒尺寸、通道流量和液相流变特性对微粒聚集的影响规律。结果表明,在剪切稀化流体羧甲基纤维素钠(CMC)水溶液中,随着通道流量和颗粒粒径增大,微颗粒聚集位置逐渐向剪切速率较高的一侧偏移;随着CMC质量分数增加,聚集位置不断向剪切速率较低的一侧偏移。利用求解的幂律型剪切稀化流体速度和剪切速率方程,结合对微颗粒的受力分析,证明稠度系数越大,聚集位置越偏向剪切速率较低处;剪切稀化特性越强,聚集位置越偏向剪切速率较高处,说明在幂律型剪切稀化流体中的黏度变化是微颗粒发生特殊迁移聚集行为的一个重要原因。     

Conjugate transport in polymer melt flow through extrusion dies

A numerical study is carried out on the conjugate thermal transport in polymer and food melts flowing through extrusion dies. The simulation is performed to determine the influence of conduction through the die wall and of the thermal boundary conditions on the transport in the fluid and on the conditions at the outlet. An extrusion die with a uniform temperature or heat transfer coefficient specified at the outer surface is considered. It is found that, because of conduction in the solid wall, important physical variables such as centerline velocity, pressure drop, bulk temperature of the fluid and shear experienced by the fluid are strongly affected by the boundary conditions, as well as by the wall thermal conductivity and thickness. Channels of different geometries are used for the study. The flow in a circular straight tube with constant wall thickness is studied first. Flow and thermal transport in different, constricted, channels are studied next. Different wall materials are also considered. Comparisons with some experimental results are presented, indicating good agreement. The fluids considered in this study are highly viscous, polymer melts. Due to high viscous dissipation and temperature-dependent viscosity, the flow and heat transfer are coupled and the problem is quite complicated. The results show that, for some operating conditions, the bulk temperature can be high enough to cause significant heat transfer from the fluid to the wall. The downstream variation in the pressure and temperature are calculated. The thermal boundary conditions are found to have a strong influence on the temperature field and thus on the flow. The general dependence of pressure drop on temperature, flow rate, and geometry is investigated. Several other basic aspects of this problem are also discussed.     

Effects of Viscous Dissipation on Heat Transfer between an Array of Long Circular Cylinders and Power Law Fluids

The free surface model has been combined with the equations of motion and of thermal energy to investigate the role of viscous dissipation on heat transfer between banks of long cylinders and power law (shear‐thinning and shear‐thickening) fluids. The equations of motion cast in the stream function/vorticity formulation have been solved numerically using a second‐order accurate finite difference method to obtain extensive information on the behaviour of local and surface‐averaged Nusselt numbers over a range of Reynolds numbers 1 – 500, for a wide range of power law indices (0.4 ≤ n ≤ 2.0), Brinkman numbers (0 ≤ Br ≤ 5) and Prandtl numbers (Pr = 1, 1000) at two representative solid volume fractions corresponding to the porosities of e = 0.4 and 0.9. Two different thermal boundary conditions are considered at the cylinder surface: constant temperature (CT) and constant heat flux (CHF). The results presented herein provide a fundamental knowledge about the influence of viscous dissipation on the heat transfer characteristics. The results reported herein further show that the effect of Brinkman number on heat transfer is strongly conditioned by the thermal boundary condition, Prandtl number and the power law index.     

Apparent viscosity of a fluid–gas mixture

The inertia free flow of a one-dimensional, isothermal fluid–gas mixture in a tube of constant radius is analyzed. The fluid is viscous, non-Newtonian, and incompressible; the gas is inviscid and compressible. Integration of the equations of continuity, momentum, and state enable the prediction of axial pressure, velocity, density, volumetric flow rate, and shear–stress profiles. Departures from corresponding profiles observed in the flow of non-Newtonian power-law fluids are evident. The apparent viscosity of the fluid–gas mixture is computed and compared to that of the fluid alone. A reduction in apparent viscosity is noted. Previously reported experimental evidence of a reduction in viscosity in a non-Newtonian fluid–gas mixture is recalled and it is claimed that the physical model presented here is capable of explaining the observed reduction in apparent viscosity.     

Conduction and dissipation in the shearing flow of granular materials modeled as non-Newtonian fluids

After providing a brief review of the constitutive modeling of the stress tensor for granular materials using non-Newtonian fluid models, we study the flow between two horizontal flat plates. It is assumed that the granular media behaves as a non-Newtonian fluid (of the Reiner-Rivlin type); we use the constitutive relation derived by Rajagopal and Massoudi [Rajagopal, K. R. and M. Massoudi, “A Method for measuring material moduli of granular materials: flow in an orthogonal rheometer,” Topical Report, DOE/PETC/TR-90/3, 1990] which can predict the normal stress differences. The lower plate is fixed and heated, and the upper plate (which is at a lower temperature than the lower plate) is set into motion with a constant velocity. The steady fully developed flow and the heat transfer equations are made dimensionless and are solved numerically; the effects of different dimensionless numbers and viscous dissipation are discussed.     

Influence of carrier fluid on the electrokinetic and rheological properties of shear thickening fluids

This paper presents a study on the influence of hydroxyl groups and oxygen atoms together with chain length and branching of carrier fluid on the rheological and electrokinetic properties of shear thickening fluid (STF). An STF is non-Newtonian fluid behaviour in which the increase of viscosity increases with the applied shear rate. Ethylene glycol, triethylene glycol, 1,3-propanediol, glycerin, poly(propylene glycol) of different molecular weight and poly(propylene glycol) triol were used as the carrier fluids (dispersants). Silica powder with an average particle size of 100 nm was used as the solid phase. Zeta potential, particle size distribution (by DLS technique), steady-state and dynamic rheological measurements were conducted. Experimental results indicate that a different amount of hydroxyl groups and oxygen atoms together with chain length and branching of carrier fluids have a significant influence on the intermolecular interactions thereby and on the rheological properties of suspensions. Depending on the composition, it is possible to control rheological properties. The use of a suitable carrier fluid allows the required pattern flow to be obtained, from Newtonian through shear thinning to shear thickening, given specific shear conditions.     

Fluid flow stability analysis of multilayer fiber drawing

We here investigate drawing of multi-layered Newtonian and non-Newtonian fluid fibers, drawn under isothermal and non-isothermal conditions. We first develop one-dimensional equations governing mass, momentum, and energy balances and solve them numerically to obtain steady state draw root shape, velocity, and temperature profiles. These solutions are then used to perform linear stability analysis. For the case of isothermal draw, the system displays an oscillatory instability when the draw ratio (ratio of cross-sectional areas of fiber at the entrance and exit of the drawing) is higher than a critical draw ratio (highest stable draw ratio) of about 20.21. Investigation of stability behavior under non-isothermal draw conditions is performed by considering radiative heating and convective cooling. Employing only radiative heating enhances the critical draw ratio, and simultaneous heating and convective cooling increase the critical draw ratio even further. For the case of simultaneous heating and cooling, with increasing convective cooling strength, the critical draw ratio first increases, reaches a maximum, and then gradually decreases. However, with only convective cooling, the critical draw ratio decreases with an increase in convective cooling strength. We also find that the stabilizing effect of a non-isothermal operation can be enhanced by considering fluids with higher viscosity sensitivity to temperature, increasing the maximum temperature, and for sharper attenuation of the fiber cross-sectional area with length. For the case of isothermal drawing of non-Newtonian fluid fibers, the system has a higher critical draw ratio for shear thickening fluids (power-law exponent, n>1). In contrast, the use of a shear thinning fluid (n<1) reduces the critical draw ratio. Consideration of a non-isothermal operation of non-Newtonian fluid fibers reveals that the critical draw ratio is primarily determined by the non-Newtonian behavior rather than the non-isothermal drawing.     

凝胶纺三元聚丙烯腈原液的流变行为

研究了聚丙烯腈／二甲基亚砜／水三元纺丝原液在不同的含水量、聚丙烯腈浓度和温度下的流变性能,获得了零切粘度,表观粘度,非牛顿指数和结构粘度指数对于原液含水量、聚丙烯腈浓度和温度的依赖关系。该溶液是一种剪切变稀的非牛顿流体。随着含水量的增加,零切粘度、表观粘度和结构粘度指数增加,非牛顿指数下降。随着聚丙烯腈浓度的增加,原液的袁观粘度和结构粘度指数增加,非牛顿指数下降。原液的流动性和可纺性随温度提高而增加。     

Viscous dissipation in capillary flow of rigid PVC and PVC degradation

The steady state, non-isothermal behavior of rigid polyvinyl chloride melt, flowing in capillaries of circular cross-section, was investigated by solving, with the aid of a digital computer, the momentum and energy balance equations. It was assumed that the polymer melt can be described by the “Power Law” constitutive equation. The shear rate, temperature and pressure dependent properties of the fluid were obtained experimentally. The effects of the thermal degradation of PVC on its viscosity, were also introduced in the equations of momentum and energy. The velocity, temperature and pressure profiles, obtained for both adiabatic flow and flow through a tube of constant wall temperature, indicate that considerable heating of the melt, due to viscous dissipation, can be achieved at moderate flow rates. Thermal degradation occurs in the capillary under certain conditions of temperature history and residence time of the fluid. The results of this work are in fair agreement with experimental results in this area.     

低气速条件下CO_2在牛顿及非牛顿流体中气含率

实验测定了低气速下CO2气泡群在牛顿流体、剪切变稀流体及黏弹性流体中的气含率。讨论了流体的流变性、质量分数及表观气速对气含率的影响。结果表明:在3种不同性质的流体中,气含率均随表观气速的增大而增大。同时发现流体性质对气含率具有不同的影响:对于牛顿流体,表观气速较低时,质量分数对气含率影响可忽略;对于非牛顿流体,气含率随着流动指数n的减小而减小,即剪切变稀效应对气含率有负作用,而黏弹性对气含率的影响可忽略。气含率是气液传质过程设计中最重要的参数,因此研究结果为进一步研究CO2气泡群在非牛顿流体中的传质奠定了一定基础。     

Investigations of heat transfer and pressure drop between parallel channels with pseudoplastic and dilatant fluids

Central to the problem of heat exchangers design is the prediction of pressure drop and heat transfer in the noncircular exchanger duct passages such as parallel channels. Numerical solutions for laminar fully developed flow are presented for the pressure drop (friction factor times Reynolds number) and heat transfer (Nusselt numbers) with thermal boundary conditions [constant heat flux (CHF) and constant wall temperature (CWT) ] for a pseudoplastic and dilatant non‐Newtonian fluid flowing between infinite parallel channels. A shear rate parameter could be used for the prediction of the shear rate range for a specified set of operating conditions that has Newtonian behavior at low shear rates, power law behavior at high shear rates, and a transition region in between. Numerical results of the Nusselt number [constant heat flux (CHF) and constant wall temperature (CWT) ] and the product of the friction factor and Reynolds number for the Newtonian region were compared with the literature values showing agreement within 0.36% in the Newtonian region. For pseudoplastic and dilatant non‐Newtonian fluids, the modified power law model is recommended to use because the fluid properties have big discrepancies between the power law model and the actual values in low and medium range of shear rates. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3601–3608, 2003     

Selection and design of aerobic bioreactors

Compared to chemical reactors, there are additional requirements to be considered when selecting and designing a bioreactor. The cultivated organisms and most of the desired products are to a greater or lesser extent sensitive to temperature, pH and Shear stress. Furthermore, sterilization often plays an important role in maintaining a monoseptic process. Many design procedures for chemical reactors can be applied but requirements which are relevant to the biological system are sometimes decisive. Consequently, it is useful to first consider the essential features of the organisms with respect to the selection and design of bioreactors. Attention must be paid to the fermentation medium because its flow behaviour can range from slightly viscous and Newtonian to highly viscous, non-Newtonian. Many papers deal with low viscosity fermentation broths [1–5]. However, little is known about the design of bioreactors for highly viscous non-Newtonian liquids. Fundamentals for the design of bioreactors are presented. It has been attempted to apply theoretical equations suitable for both, low viscosity Newtonian and high viscosity non-Newtonian fermentation broths. Apart from the calculation procedure for the OTR-values, the difference between global and local values within bioreactor is demonstrated by means of velocity and shear stress profiles. Special requirements for bioreactors such as prevention of excessive foaming, shear sensitivity of micro-organisms and cell-lines and effective sterilization are also discussed.     

Combined effects of internal heat generation and higher order chemical reaction on the non‐darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium

In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two‐dimensional non‐Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear‐coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non‐dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction. © 2011 Canadian Society for Chemical Engineering     

Non-Isothermal mixing of rheologically complex fluids with close-clearance impellers: Effect of natural convection

Transient heat transfer in a mechanically agitated vessel is studied in the case of an anchor and an helical ribbon impeller using Newtonian and shear thinning fluids. Temperature stratification is found more pronounced with the anchor, making this impeller clearly inadequate for heat transfer. The impact of natural convection is evaluated first using the classical Gr/Re² ratio. It is shown that the use of this criterion in viscous mixing is somewhat misleading. A new Grashof number is then proposed to assess the significance of the viscous and buoyancy effects in non-isothermal, non-Newtonian mixing applications. It is shown that the interpretation of this new number is strongly related to the concept of process viscosity.     

Laminar natural convection heat transfer from a slender vertical cone to a power-law fluid

A theoretical analysis of laminar natural convection heat transfer from a slender vertical cone to a power-law fluid has been done by the approximate integral method. Assuming unequal thermal and momentum boundary layer thicknesses, and using the appropriate boundary and compatibility conditions, a “similar” solution of the boundary layer equations has been obtained for high Prandtl numbers. Due to lack of experimental data for power-law fluids, a comparison of the predictions of the present analysis has been done with the experimental data available for Newtonian fluids and good agreement has been found.     

Convective heat transfer for power law fluids in packed and fluidised beds of spheres

The forced convection heat transfer characteristics for an incompressible and steady flow of power law liquids in fixed and extended beds of spherical particles has been studied numerically. The sphere-sphere hydrodynamic interactions have been accounted for by using a simple cell model. Within the framework of such a cell model, the momentum and energy equations have been solved using a finite difference method to obtain the velocity and temperature fields. Extensive numerical estimates of the local and average Nusselt numbers as functions of the physical, rheological and kinematic variables have been presented and discussed for the two commonly employed thermal boundary conditions. In broad terms, the Nusselt number for power law fluids (both shear-thinning and shear-thickening conditions) normalized with respect to the corresponding value for a Newtonian fluid shows weak additional dependence on the power law flow behaviour index. The shear-thinning behaviour is seen to promote heat transfer and as expected the shear-thickening behaviour impedes heat transfer in fixed and fluidised beds. All in all, the present results encompass wide ranges of conditions as follows: Reynolds number: 1-500; Peclet number: 1-500; bed voidage: 0.4-0.8 and the flow behaviour index: 0.5-1.8 thereby covering extremely shear-thinning and shear-thickening types of fluid behaviours. The paper is concluded by presenting detailed comparisons with the limited analytical and/or experimental results available for liquid-solid mass transfer in such systems.     

Shear rate dependence of thermal conductivity and its effect on heat transfer in a Non-Newtonian flow system

The purpose of this research was to investigate the extent to which the thermal conductivity of non-Newtonian fluids is affected by fluid motion, and then the effect of this shear-rate-dependent thermal conductivity, measured in Lee [1995], on the heat transfer for a typical convective system. Such information would have important implications in the design and analysis of non-Newtonian thermal systems such as are found in food processing operations, polymer processing, paint manufacturing, biological systems and many others. A simple parallel plate flow model with temperature-independent properties gave increases in heat transfer on the order of 30–80 % compared to the heat transfer with shear-rate-independent thermal conductivity in Newtonian fluid flow over the entire temperature range (20–50 °C) of CMC solutions depending on the inlet average velocity due to the effect of the shear-rate-dependent thermal conductivity.